B-IncStrDB

Exploiting superspace to clarify vacancy and Al/Si ordering in mullite

Authors:

Klar, Paul Benjamin; Etxebarria, Inigo; Madariaga, Gotzon

Journal:

IUCrJ 5 497-509 (2018)

DOI:

https://doi.org/10.1107/S2052252518007467

B-IncStrDB ID: 13462ERV71a Entry date: 2018-06-19 Last revision: 2021-12-12

SA1

Chemical data

Common Name: Mullite [ Help ]

Structural Formula Sum: Al4.857 O9.571 Si1.143 [ Help ]

Formula weight: 316.3 Da [ Help ]

Compound Source: Sigma Aldrich [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pbam(α01/2)0ss [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,-x2,x3,x3-x4+1/2
3	-x1+1/2,x2+1/2,-x3,-x4+1/2
4	x1+1/2,-x2+1/2,-x3,-x3+x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x3+x4+1/2
7	x1+1/2,-x2+1/2,x3,x4+1/2
8	-x1+1/2,x2+1/2,x3,x3-x4

a: 7.5787(7) Å [ Help ]

b: 7.6707(4) Å [ Help ]

c: 2.88360(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 167.635(19) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.298800	0.000000	0.500000

Z: 1 [ Help ]

Cell determination reflection Nb.: 2027 [ Help ]

θ(min) for cell determination: 4.06 ° [ Help ]

θ(max) for cell determination: 31.88 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.08 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Absorption correction remarks: CrysAlisPro 1.171.38.46 (Rigaku Oxford Diffraction, 2015) Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm. [ Help ]

Minimum transmission factor: 0.834 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 678 [ Help ]

Nb. of observed reflections: 555 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0371 [ Help ]

wR(obs): 0.1028 [ Help ]

R(all): 0.0384 [ Help ]

wR(all): 0.1044 [ Help ]

S(all): 1.01 [ Help ]

S(obs): 1.12 [ Help ]

Nb. of reflections: 678 [ Help ]

Nb. of parameters: 101 [ Help ]

Number of constraints: 33 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0081000002I²) [ Help ]

Δ/σ(max): 0.0003 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 0.37 e_Å^-3 [ Help ]

Δρ(min): -0.33 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Al1	Al	0	0	0	Uani	0.0109(3)	2	1	d	?	?	?
Al2	Al	0.14896(9)	0.33959(6)	0.5	Uani	0.0121(3)	4	0.5	d	?	?	?
Si2	Si	0.14896(9)	0.33959(6)	0.5	Uani	0.0121(3)	4	0.286(2)	d	?	?	?
Al3	Al	0.2630(4)	0.2056(3)	0.5	Uani	0.0112(7)	4	0.214(2)	d	?	?	?
O1	O	0.35894(15)	0.42166(14)	0.5	Uani	0.0168(4)	4	1	d	?	?	?
O2	O	0.12752(15)	0.21786(19)	0	Uani	0.0175(4)	4	1	d	?	?	?
O3	O	0	0.5	0.5	Uani	0.020(3)	2	0.357(7)	d	?	?	?
O4	O	0.449(2)	0.0509(12)	0.5	Uani	0.017(3)	4	0.214(2)	d	?	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0144(7)	0.0105(4)	0.0078(4)	0.00108(19)
Al2	Al	0.0151(6)	0.0119(4)	0.0092(4)	-0.00092(17)
Si2	Si	0.0151(6)	0.0119(4)	0.0092(4)	-0.00092(17)
Al3	Al	0.0116(16)	0.0138(10)	0.0082(8)	0.0005(9)
O1	O	0.0215(9)	0.0216(5)	0.0073(4)	-0.0051(4)
O2	O	0.0210(8)	0.0169(6)	0.0145(4)	-0.0057(4)
O3	O	0.019(7)	0.017(6)	0.025(3)	0.000(3)
O4	O	0.025(9)	0.009(4)	0.016(2)	-0.0012(17)

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_1
1	1

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al2	0.5
Si2	0.286(2)
Al3	0.214(2)
O3	0.357(7)
O4	0.214(2)

Definition of the occupation Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Wave vector code
Al2o1	Al2	1
Si2o1	Si2	1
Al3o1	Al3	1
O3o1	O3	1
O4o1	O4	1

Occupation Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al2o1	0.0486(5)	0.01396(14)
Si2o1	0.0486(5)	0.01396(14)
Al3o1	-0.0891(9)	-0.0479(5)
O3o1	-0.01838(19)	0
O4o1	-0.0674(7)	-0.0755(8)

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1
Si2x1	Si2	x	1
Si2y1	Si2	y	1
Si2z1	Si2	z	1
Al3x1	Al3	x	1
Al3y1	Al3	y	1
Al3z1	Al3	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	0	0
Al1y1	0	0
Al1z1	0	-0.00471(7)
Al2x1	0.00050(3)	-0.00131(3)
Al2y1	-0.00010(3)	-0.00152(3)
Al2z1	0	0
Si2x1	0.00050(3)	-0.00131(3)
Si2y1	-0.00010(3)	-0.00152(3)
Si2z1	0	0
Al3x1	0.0009(2)	-0.00078(15)
Al3y1	0.00052(18)	-0.00089(13)
Al3z1	0	0
O1x1	-0.00180(6)	-0.00230(5)
O1y1	0.00428(6)	0.00234(5)
O1z1	0	0
O2x1	0	0
O2y1	0	0
O2z1	-0.00653(12)	-0.00285(11)
O3x1	0	-0.0029(5)
O3y1	0	0.0034(4)
O3z1	0	0
O4x1	-0.0015(10)	0.0004(10)
O4y1	0.0006(8)	0.0000(6)
O4z1	0	0

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al2U111	Al2	U11	1
Al2U221	Al2	U22	1
Al2U331	Al2	U33	1
Al2U121	Al2	U12	1
Al2U131	Al2	U13	1
Al2U231	Al2	U23	1
Si2U111	Si2	U11	1
Si2U221	Si2	U22	1
Si2U331	Si2	U33	1
Si2U121	Si2	U12	1
Si2U131	Si2	U13	1
Si2U231	Si2	U23	1
Al3U111	Al3	U11	1
Al3U221	Al3	U22	1
Al3U331	Al3	U33	1
Al3U121	Al3	U12	1
Al3U131	Al3	U13	1
Al3U231	Al3	U23	1
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O3U111	O3	U11	1
O3U221	O3	U22	1
O3U331	O3	U33	1
O3U121	O3	U12	1
O3U131	O3	U13	1
O3U231	O3	U23	1
O4U111	O4	U11	1
O4U221	O4	U22	1
O4U331	O4	U33	1
O4U121	O4	U12	1
O4U131	O4	U13	1
O4U231	O4	U23	1

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0	0
Al1U221	0	0
Al1U331	0	0
Al1U121	0	0
Al1U131	0.00016(8)	0
Al1U231	-0.00025(6)	0
Al2U111	-0.00093(15)	0.00014(13)
Al2U221	-0.00094(11)	0.00158(9)
Al2U331	0.00065(9)	0.00044(7)
Al2U121	0.00014(8)	-0.00005(8)
Al2U131	0	0
Al2U231	0	0
Si2U111	-0.00093(15)	0.00014(13)
Si2U221	-0.00094(11)	0.00158(9)
Si2U331	0.00065(9)	0.00044(7)
Si2U121	0.00014(8)	-0.00005(8)
Si2U131	0	0
Si2U231	0	0
Al3U111	0.0022(9)	0.0018(6)
Al3U221	0.0035(6)	0.0012(4)
Al3U331	0.0012(5)	0.0005(3)
Al3U121	0.0004(5)	-0.0001(4)
Al3U131	0	0
Al3U231	0	0
O1U111	-0.0008(2)	-0.0010(2)
O1U221	0.0005(2)	0.00018(19)
O1U331	0.00013(13)	0.00004(14)
O1U121	0.00093(16)	0.00060(17)
O1U131	0	0
O1U231	0	0
O2U111	0	0
O2U221	0	0
O2U331	0	0
O2U121	0	0
O2U131	-0.00041(16)	-0.00009(16)
O2U231	-0.00019(13)	-0.00014(13)
O3U111	-0.002(3)	0
O3U221	0.003(3)	0
O3U331	0.0042(10)	0
O3U121	0	0
O3U131	0	0
O3U231	0	0
O4U111	0.006(4)	0.003(4)
O4U221	0.000(3)	0.0009(19)
O4U331	-0.0030(11)	0.0001(11)
O4U121	0	0
O4U131	0	0
O4U231	0	0

SA2

Chemical data

Common Name: Mullite [ Help ]

Structural Formula Sum: Al4.832 O9.584 Si1.168 [ Help ]

Formula weight: 316.5 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pbam(α01/2)0ss [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,-x2,x3,x3-x4+1/2
3	-x1+1/2,x2+1/2,-x3,-x4+1/2
4	x1+1/2,-x2+1/2,-x3,-x3+x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x3+x4+1/2
7	x1+1/2,-x2+1/2,x3,x4+1/2
8	-x1+1/2,x2+1/2,x3,x3-x4

a: 7.577(2) Å [ Help ]

b: 7.6727(18) Å [ Help ]

c: 2.8804(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 167.46(8) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.301000	0.000000	0.500000

Z: 1 [ Help ]

Cell determination reflection Nb.: 1568 [ Help ]

θ(max) for cell determination: 31.98 ° [ Help ]

θ(min) for cell determination: 4.06 ° [ Help ]

Maximum transmission factor: 1 [ Help ]

Minimum transmission factor: 0.761 [ Help ]

Absorption correction type: multi-scan [ Help ]

μ: 1.082 mm^-1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Refinement details

Total nb. of reflections: 768 [ Help ]

Nb. of observed reflections: 544 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

R(obs): 0.0312 [ Help ]

wR(obs): 0.0846 [ Help ]

R(all): 0.0347 [ Help ]

wR(all): 0.0885 [ Help ]

S(all): 1.08 [ Help ]

S(obs): 1.27 [ Help ]

Nb. of reflections: 768 [ Help ]

Nb. of parameters: 101 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0035999999I²) [ Help ]

Δ/σ(max): 0.0004 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 0.35 e_Å^-3 [ Help ]

Δρ(min): -0.39 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Number of constraints: 33 [ Help ]

Refinement based on: Fsqd [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Al1	Al	0	0	0	Uani	0.00863(17)	2	1	d	?	?	?
Al2	Al	0.14885(5)	0.33985(4)	0.5	Uani	0.00933(17)	4	0.5	d	?	?	?
Si2	Si	0.14885(5)	0.33985(4)	0.5	Uani	0.00933(17)	4	0.2920(19)	d	?	?	?
Al3	Al	0.2626(2)	0.2043(2)	0.5	Uani	0.0086(4)	4	0.2080(19)	d	?	?	?
O1	O	0.35912(10)	0.42179(11)	0.5	Uani	0.0151(2)	4	1	d	?	?	?
O2	O	0.12766(11)	0.21705(13)	0	Uani	0.0161(2)	4	1	d	?	?	?
O3	O	0	0.5	0.5	Uani	0.0196(19)	2	0.376(6)	d	?	?	?
O4	O	0.4483(9)	0.0466(9)	0.5	Uani	0.0114(17)	4	0.2080(19)	d	?	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0085(3)	0.0089(3)	0.0085(3)	0.00056(12)
Al2	Al	0.0070(3)	0.0107(3)	0.0102(3)	-0.00055(10)
Si2	Si	0.0070(3)	0.0107(3)	0.0102(3)	-0.00055(10)
Al3	Al	0.0066(7)	0.0109(8)	0.0084(7)	0.0005(5)
O1	O	0.0147(4)	0.0221(4)	0.0086(4)	-0.0079(3)
O2	O	0.0159(4)	0.0173(4)	0.0150(4)	-0.0072(3)
O3	O	0.008(4)	0.019(4)	0.0317(18)	0.0023(18)
O4	O	0.005(4)	0.011(3)	0.0182(18)	0.0004(12)

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_1
1	1

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al2	0.5
Si2	0.2920(19)
Al3	0.2080(19)
O3	0.376(6)
O4	0.2080(19)

Definition of the occupation Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Wave vector code
Al2o1	Al2	1
Si2o1	Si2	1
Al3o1	Al3	1
O3o1	O3	1
O4o1	O4	1

Occupation Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al2o1	0.0341(3)	0.00987(8)
Si2o1	0.0341(3)	0.00987(8)
Al3o1	-0.0625(5)	-0.0339(3)
O3o1	-0.01212(10)	0
O4o1	-0.0470(4)	-0.0533(5)

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1
Si2x1	Si2	x	1
Si2y1	Si2	y	1
Si2z1	Si2	z	1
Al3x1	Al3	x	1
Al3y1	Al3	y	1
Al3z1	Al3	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	0	0
Al1y1	0	0
Al1z1	0	-0.00305(6)
Al2x1	0.00037(2)	-0.00084(2)
Al2y1	-0.00012(2)	-0.00096(2)
Al2z1	0	0
Si2x1	0.00037(2)	-0.00084(2)
Si2y1	-0.00012(2)	-0.00096(2)
Si2z1	0	0
Al3x1	0.00063(11)	-0.00064(9)
Al3y1	-0.00008(10)	-0.00081(9)
Al3z1	0	0
O1x1	-0.00121(4)	-0.00157(4)
O1y1	0.00276(4)	0.00164(4)
O1z1	0	0
O2x1	0	0
O2y1	0	0
O2z1	-0.00431(11)	-0.00194(10)
O3x1	0	-0.0017(3)
O3y1	0	0.0018(3)
O3z1	0	0
O4x1	-0.0014(6)	0.0004(4)
O4y1	-0.0008(6)	-0.0013(4)
O4z1	0	0

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al2U111	Al2	U11	1
Al2U221	Al2	U22	1
Al2U331	Al2	U33	1
Al2U121	Al2	U12	1
Al2U131	Al2	U13	1
Al2U231	Al2	U23	1
Si2U111	Si2	U11	1
Si2U221	Si2	U22	1
Si2U331	Si2	U33	1
Si2U121	Si2	U12	1
Si2U131	Si2	U13	1
Si2U231	Si2	U23	1
Al3U111	Al3	U11	1
Al3U221	Al3	U22	1
Al3U331	Al3	U33	1
Al3U121	Al3	U12	1
Al3U131	Al3	U13	1
Al3U231	Al3	U23	1
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O3U111	O3	U11	1
O3U221	O3	U22	1
O3U331	O3	U33	1
O3U121	O3	U12	1
O3U131	O3	U13	1
O3U231	O3	U23	1
O4U111	O4	U11	1
O4U221	O4	U22	1
O4U331	O4	U33	1
O4U121	O4	U12	1
O4U131	O4	U13	1
O4U231	O4	U23	1

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0	0
Al1U221	0	0
Al1U331	0	0
Al1U121	0	0
Al1U131	0.00017(6)	0
Al1U231	-0.00011(7)	0
Al2U111	-0.00021(8)	0.00017(7)
Al2U221	-0.00026(8)	0.00118(8)
Al2U331	0.00094(8)	0.00039(7)
Al2U121	0.00012(6)	-0.00004(6)
Al2U131	0	0
Al2U231	0	0
Si2U111	-0.00021(8)	0.00017(7)
Si2U221	-0.00026(8)	0.00118(8)
Si2U331	0.00094(8)	0.00039(7)
Si2U121	0.00012(6)	-0.00004(6)
Si2U131	0	0
Si2U231	0	0
Al3U111	0.0008(4)	0.0005(3)
Al3U221	0.0009(4)	0.0003(4)
Al3U331	-0.0013(4)	-0.0007(3)
Al3U121	0.0003(3)	-0.0005(3)
Al3U131	0	0
Al3U231	0	0
O1U111	-0.00058(17)	-0.00062(17)
O1U221	0.00012(18)	0.00009(18)
O1U331	0.00028(13)	0.00023(14)
O1U121	0.00069(14)	0.00071(13)
O1U131	0	0
O1U231	0	0
O2U111	0	0
O2U221	0	0
O2U331	0	0
O2U121	0	0
O2U131	-0.00013(12)	-0.00004(12)
O2U231	-0.00021(13)	-0.00020(13)
O3U111	-0.001(3)	0
O3U221	0.000(2)	0
O3U331	0.0044(10)	0
O3U121	0	0
O3U131	0	0
O3U231	0	0
O4U111	-0.001(2)	-0.0014(15)
O4U221	0.0004(18)	-0.0008(12)
O4U331	-0.0015(10)	-0.0022(9)
O4U121	0	0
O4U131	0	0
O4U231	0	0

SA3

Chemical data

Structural Formula Sum: Al4.868 O9.566 Si1.132 [ Help ]

Formula weight: 316.2 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pbam(α01/2)0ss [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,-x2,x3,x3-x4+1/2
3	-x1+1/2,x2+1/2,-x3,-x4+1/2
4	x1+1/2,-x2+1/2,-x3,-x3+x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x3+x4+1/2
7	x1+1/2,-x2+1/2,x3,x4+1/2
8	-x1+1/2,x2+1/2,x3,x3-x4

a: 7.5768(13) Å [ Help ]

b: 7.6760(16) Å [ Help ]

c: 2.8833(12) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 167.69(8) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.306800	0.000000	0.500000

Z: 1 [ Help ]

Cell determination reflection Nb.: 982 [ Help ]

θ(max) for cell determination: 31.9 ° [ Help ]

θ(min) for cell determination: 4.06 ° [ Help ]

Maximum transmission factor: 1 [ Help ]

Minimum transmission factor: 0.585 [ Help ]

Absorption correction type: multi-scan [ Help ]

μ: 1.079 mm^-1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

Refinement details

Total nb. of reflections: 667 [ Help ]

Nb. of observed reflections: 382 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

R(obs): 0.0374 [ Help ]

wR(obs): 0.1056 [ Help ]

R(all): 0.0423 [ Help ]

wR(all): 0.1105 [ Help ]

S(all): 1.44 [ Help ]

S(obs): 1.95 [ Help ]

Nb. of reflections: 667 [ Help ]

Nb. of parameters: 101 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0025000002I²) [ Help ]

Δ/σ(max): 0.0001 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 0.43 e_Å^-3 [ Help ]

Δρ(min): -0.46 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Number of constraints: 33 [ Help ]

Refinement based on: Fsqd [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Al1	Al	0	0	0	Uani	0.0089(3)	2	1	d	?	?	?
Al2	Al	0.14905(5)	0.34005(5)	0.5	Uani	0.0096(3)	4	0.5	d	?	?	?
Si2	Si	0.14905(5)	0.34005(5)	0.5	Uani	0.0096(3)	4	0.283(3)	d	?	?	?
Al3	Al	0.2624(2)	0.2058(2)	0.5	Uani	0.0105(6)	4	0.217(3)	d	?	?	?
O1	O	0.35841(11)	0.42165(16)	0.5	Uani	0.0166(4)	4	1	d	?	?	?
O2	O	0.12754(11)	0.21837(15)	0	Uani	0.0173(4)	4	1	d	?	?	?
O3	O	0	0.5	0.5	Uani	0.017(3)	2	0.349(8)	d	?	?	?
O4	O	0.4534(10)	0.0482(9)	0.5	Uani	0.0120(19)	4	0.217(3)	d	?	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0128(3)	0.0056(3)	0.0082(7)	0.00085(13)
Al2	Al	0.0117(4)	0.0073(3)	0.0099(8)	-0.00061(13)
Si2	Si	0.0117(4)	0.0073(3)	0.0099(8)	-0.00061(13)
Al3	Al	0.0131(7)	0.0114(8)	0.0069(16)	0.0008(6)
O1	O	0.0200(5)	0.0196(5)	0.0101(10)	-0.0087(3)
O2	O	0.0211(4)	0.0125(5)	0.0183(9)	-0.0060(3)
O3	O	0.019(5)	0.008(4)	0.023(4)	-0.006(2)
O4	O	0.011(4)	0.004(3)	0.020(3)	-0.0017(17)

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_1
1	1

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al2	0.5
Si2	0.283(3)
Al3	0.217(3)
O3	0.349(8)
O4	0.217(3)

Definition of the occupation Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Wave vector code
Al2o1	Al2	1
Si2o1	Si2	1
Al3o1	Al3	1
O3o1	O3	1
O4o1	O4	1

Occupation Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al2o1	0.0129(2)	0.00382(7)
Si2o1	0.0129(2)	0.00382(7)
Al3o1	-0.0236(4)	-0.0131(2)
O3o1	-0.00379(7)	0
O4o1	-0.0173(3)	-0.0207(4)

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1
Si2x1	Si2	x	1
Si2y1	Si2	y	1
Si2z1	Si2	z	1
Al3x1	Al3	x	1
Al3y1	Al3	y	1
Al3z1	Al3	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	0	0
Al1y1	0	0
Al1z1	0	-0.00138(8)
Al2x1	0.00016(4)	-0.00047(4)
Al2y1	-0.00008(2)	-0.00047(2)
Al2z1	0	0
Si2x1	0.00016(4)	-0.00047(4)
Si2y1	-0.00008(2)	-0.00047(2)
Si2z1	0	0
Al3x1	0.00049(17)	0.00004(15)
Al3y1	0.00029(8)	-0.00026(9)
Al3z1	0	0
O1x1	-0.00058(8)	-0.00072(8)
O1y1	0.00129(4)	0.00073(4)
O1z1	0	0
O2x1	0	0
O2y1	0	0
O2z1	-0.00207(15)	-0.00109(14)
O3x1	0	-0.0016(5)
O3y1	0	0.0013(3)
O3z1	0	0
O4x1	-0.0008(7)	0.0003(5)
O4y1	-0.0007(5)	-0.0004(3)
O4z1	0	0

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al2U111	Al2	U11	1
Al2U221	Al2	U22	1
Al2U331	Al2	U33	1
Al2U121	Al2	U12	1
Al2U131	Al2	U13	1
Al2U231	Al2	U23	1
Si2U111	Si2	U11	1
Si2U221	Si2	U22	1
Si2U331	Si2	U33	1
Si2U121	Si2	U12	1
Si2U131	Si2	U13	1
Si2U231	Si2	U23	1
Al3U111	Al3	U11	1
Al3U221	Al3	U22	1
Al3U331	Al3	U33	1
Al3U121	Al3	U12	1
Al3U131	Al3	U13	1
Al3U231	Al3	U23	1
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O3U111	O3	U11	1
O3U221	O3	U22	1
O3U331	O3	U33	1
O3U121	O3	U12	1
O3U131	O3	U13	1
O3U231	O3	U23	1
O4U111	O4	U11	1
O4U221	O4	U22	1
O4U331	O4	U33	1
O4U121	O4	U12	1
O4U131	O4	U13	1
O4U231	O4	U23	1

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0	0
Al1U221	0	0
Al1U331	0	0
Al1U121	0	0
Al1U131	-0.00009(13)	0
Al1U231	-0.00015(7)	0
Al2U111	-0.00075(16)	-0.00015(16)
Al2U221	-0.00040(7)	0.00055(8)
Al2U331	-0.00002(14)	0.00010(14)
Al2U121	-0.00009(9)	-0.00007(8)
Al2U131	0	0
Al2U231	0	0
Si2U111	-0.00075(16)	-0.00015(16)
Si2U221	-0.00040(7)	0.00055(8)
Si2U331	-0.00002(14)	0.00010(14)
Si2U121	-0.00009(9)	-0.00007(8)
Si2U131	0	0
Si2U231	0	0
Al3U111	0.0035(6)	0.0029(6)
Al3U221	0.0020(3)	0.0012(3)
Al3U331	0.0003(6)	0.0007(5)
Al3U121	0.0005(3)	-0.0003(3)
Al3U131	0	0
Al3U231	0	0
O1U111	-0.0007(4)	-0.0002(3)
O1U221	0.00014(17)	-0.00003(17)
O1U331	0.0002(2)	0.0003(3)
O1U121	0.00051(19)	0.00027(18)
O1U131	0	0
O1U231	0	0
O2U111	0	0
O2U221	0	0
O2U331	0	0
O2U121	0	0
O2U131	0.0000(2)	-0.0002(2)
O2U231	-0.00003(14)	-0.00012(13)
O3U111	0.000(3)	0
O3U221	-0.003(2)	0
O3U331	0.0028(16)	0
O3U121	0	0
O3U131	0	0
O3U231	0	0
O4U111	0.004(2)	-0.0012(18)
O4U221	0.0032(18)	0.0006(10)
O4U331	-0.0005(18)	0.0006(14)
O4U121	0	0
O4U131	0	0
O4U231	0	0

QG

Chemical data

Common Name: Mullite [ Help ]

Structural Formula Sum: Al4.853 O9.574 Si1.147 [ Help ]

Formula weight: 316.3 Da [ Help ]

Compound Source: Sigma Aldrich [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Pbam(α01/2)0ss [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,-x2,x3,x3-x4+1/2
3	-x1+1/2,x2+1/2,-x3,-x4+1/2
4	x1+1/2,-x2+1/2,-x3,-x3+x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x3+x4+1/2
7	x1+1/2,-x2+1/2,x3,x4+1/2
8	-x1+1/2,x2+1/2,x3,x3-x4

a: 7.577(2) Å [ Help ]

b: 7.6738(19) Å [ Help ]

c: 2.8823(10) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 167.59(8) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.294800	0.000000	0.500000

Z: 1 [ Help ]

Cell determination reflection Nb.: 1039 [ Help ]

θ(min) for cell determination: 4.07 ° [ Help ]

θ(max) for cell determination: 31.8 ° [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 1.08 mm^-1 [ Help ]

Absorption correction type: multi-scan [ Help ]

Minimum transmission factor: 0.569 [ Help ]

Maximum transmission factor: 1 [ Help ]

Refinement details

Total nb. of reflections: 797 [ Help ]

Nb. of observed reflections: 454 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: Fsqd [ Help ]

R(obs): 0.0252 [ Help ]

wR(obs): 0.0916 [ Help ]

R(all): 0.0310 [ Help ]

wR(all): 0.0971 [ Help ]

S(all): 1.03 [ Help ]

S(obs): 1.37 [ Help ]

Nb. of reflections: 797 [ Help ]

Nb. of parameters: 101 [ Help ]

Number of constraints: 33 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(I)+0.0035999999I²) [ Help ]

Δ/σ(max): 0.0006 [ Help ]

Δ/σ(mean): 0.0000 [ Help ]

Δρ(max): 0.28 e_Å^-3 [ Help ]

Δρ(min): -0.30 e_Å^-3 [ Help ]

Extinction method: none [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	x	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Al1	Al	0	0	0	Uani	0.01054(17)	2	1	d	?	?	?
Al2	Al	0.14908(4)	0.33987(4)	0.5	Uani	0.01046(17)	4	0.5	d	?	?	?
Si2	Si	0.14908(4)	0.33987(4)	0.5	Uani	0.01046(17)	4	0.2868(17)	d	?	?	?
Al3	Al	0.26226(19)	0.2054(2)	0.5	Uani	0.0121(4)	4	0.2132(17)	d	?	?	?
O1	O	0.35879(9)	0.42178(11)	0.5	Uani	0.0165(3)	4	1	d	?	?	?
O2	O	0.12793(9)	0.21778(13)	0	Uani	0.0173(2)	4	1	d	?	?	?
O3	O	0	0.5	0.5	Uani	0.021(2)	2	0.360(5)	d	?	?	?
O4	O	0.4543(9)	0.0499(8)	0.5	Uani	0.0124(16)	4	0.2132(17)	d	?	?	?

ADP components: (Show/hide table) [ Help ]

Atom site label	Atom site symbol	U11	U22	U33	U12
Al1	Al	0.0128(3)	0.0098(3)	0.0090(3)	0.00056(12)
Al2	Al	0.0118(3)	0.0096(3)	0.0100(3)	-0.00058(10)
Si2	Si	0.0118(3)	0.0096(3)	0.0100(3)	-0.00058(10)
Al3	Al	0.0133(6)	0.0120(7)	0.0110(7)	0.0002(5)
O1	O	0.0193(4)	0.0201(4)	0.0099(5)	-0.0076(3)
O2	O	0.0208(3)	0.0155(4)	0.0155(4)	-0.0062(3)
O3	O	0.020(4)	0.017(4)	0.026(2)	-0.0076(18)
O4	O	0.015(3)	0.006(3)	0.0159(18)	-0.0020(17)

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_1
1	1

Table: (Show/hide table) [ Help ]

_jana_atom_site_occ_Fourier_absolute_site_label	_jana_atom_site_occ_Fourier_absolute
Al2	0.5
Si2	0.2868(17)
Al3	0.2132(17)
O3	0.360(5)
O4	0.2132(17)

Definition of the occupation Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Wave vector code
Al2o1	Al2	1
Si2o1	Si2	1
Al3o1	Al3	1
O3o1	O3	1
O4o1	O4	1

Occupation Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al2o1	0.0197(2)	0.00558(7)
Si2o1	0.0197(2)	0.00558(7)
Al3o1	-0.0362(5)	-0.0191(2)
O3o1	-0.00826(10)	0
O4o1	-0.0273(3)	-0.0305(4)

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Al1x1	Al1	x	1
Al1y1	Al1	y	1
Al1z1	Al1	z	1
Al2x1	Al2	x	1
Al2y1	Al2	y	1
Al2z1	Al2	z	1
Si2x1	Si2	x	1
Si2y1	Si2	y	1
Si2z1	Si2	z	1
Al3x1	Al3	x	1
Al3y1	Al3	y	1
Al3z1	Al3	z	1
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O2x1	O2	x	1
O2y1	O2	y	1
O2z1	O2	z	1
O3x1	O3	x	1
O3y1	O3	y	1
O3z1	O3	z	1
O4x1	O4	x	1
O4y1	O4	y	1
O4z1	O4	z	1

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1x1	0	0
Al1y1	0	0
Al1z1	0	-0.00201(9)
Al2x1	0.00021(3)	-0.00054(3)
Al2y1	-0.00012(3)	-0.00065(3)
Al2z1	0	0
Si2x1	0.00021(3)	-0.00054(3)
Si2y1	-0.00012(3)	-0.00065(3)
Si2z1	0	0
Al3x1	0.00049(14)	-0.00035(13)
Al3y1	0.00016(13)	-0.00060(12)
Al3z1	0	0
O1x1	-0.00079(6)	-0.00104(7)
O1y1	0.00171(6)	0.00088(6)
O1z1	0	0
O2x1	0	0
O2y1	0	0
O2z1	-0.00271(14)	-0.00114(14)
O3x1	0	-0.0007(5)
O3y1	0	0.0008(5)
O3z1	0	0
O4x1	0.0007(8)	0.0012(5)
O4y1	0.0004(8)	0.0002(4)
O4z1	0	0

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Al1U111	Al1	U11	1
Al1U221	Al1	U22	1
Al1U331	Al1	U33	1
Al1U121	Al1	U12	1
Al1U131	Al1	U13	1
Al1U231	Al1	U23	1
Al2U111	Al2	U11	1
Al2U221	Al2	U22	1
Al2U331	Al2	U33	1
Al2U121	Al2	U12	1
Al2U131	Al2	U13	1
Al2U231	Al2	U23	1
Si2U111	Si2	U11	1
Si2U221	Si2	U22	1
Si2U331	Si2	U33	1
Si2U121	Si2	U12	1
Si2U131	Si2	U13	1
Si2U231	Si2	U23	1
Al3U111	Al3	U11	1
Al3U221	Al3	U22	1
Al3U331	Al3	U33	1
Al3U121	Al3	U12	1
Al3U131	Al3	U13	1
Al3U231	Al3	U23	1
O1U111	O1	U11	1
O1U221	O1	U22	1
O1U331	O1	U33	1
O1U121	O1	U12	1
O1U131	O1	U13	1
O1U231	O1	U23	1
O2U111	O2	U11	1
O2U221	O2	U22	1
O2U331	O2	U33	1
O2U121	O2	U12	1
O2U131	O2	U13	1
O2U231	O2	U23	1
O3U111	O3	U11	1
O3U221	O3	U22	1
O3U331	O3	U33	1
O3U121	O3	U12	1
O3U131	O3	U13	1
O3U231	O3	U23	1
O4U111	O4	U11	1
O4U221	O4	U22	1
O4U331	O4	U33	1
O4U121	O4	U12	1
O4U131	O4	U13	1
O4U231	O4	U23	1

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Al1U111	0	0
Al1U221	0	0
Al1U331	0	0
Al1U121	0	0
Al1U131	0.00009(11)	0
Al1U231	-0.00009(10)	0
Al2U111	-0.00037(13)	0.00007(12)
Al2U221	-0.00059(11)	0.00067(13)
Al2U331	0.00003(12)	0.00017(12)
Al2U121	0.00001(10)	-0.00014(10)
Al2U131	0	0
Al2U231	0	0
Si2U111	-0.00037(13)	0.00007(12)
Si2U221	-0.00059(11)	0.00067(13)
Si2U331	0.00003(12)	0.00017(12)
Si2U121	0.00001(10)	-0.00014(10)
Si2U131	0	0
Si2U231	0	0
Al3U111	0.0019(5)	0.0013(5)
Al3U221	0.0026(5)	0.0018(5)
Al3U331	0.0008(5)	0.0007(4)
Al3U121	0.0010(4)	-0.0005(4)
Al3U131	0	0
Al3U231	0	0
O1U111	-0.0008(3)	-0.0003(3)
O1U221	0.0002(3)	0.0001(3)
O1U331	0.0000(2)	0.0001(2)
O1U121	0.0005(2)	0.0000(2)
O1U131	0	0
O1U231	0	0
O2U111	0	0
O2U221	0	0
O2U331	0	0
O2U121	0	0
O2U131	-0.00012(19)	-0.00023(19)
O2U231	-0.0003(2)	0.00015(19)
O3U111	-0.003(3)	0
O3U221	0.002(4)	0
O3U331	0.0015(17)	0
O3U121	0	0
O3U131	0	0
O3U231	0	0
O4U111	0.005(3)	0.0009(19)
O4U221	0.000(3)	-0.0002(15)
O4U331	-0.0012(16)	0.0002(13)
O4U121	0	0
O4U131	0	0
O4U231	0	0

Exploiting superspace to clarify vacancy and Al/Si ordering in mullite

Klar, Paul Benjamin; Etxebarria, Inigo; Madariaga, Gotzon

IUCrJ 5 497-509 (2018)

https://doi.org/10.1107/S2052252518007467

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SA1

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SA2

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SA3

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QG

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